The Extension Spaces of Nonsymmetric Classical Domains

Abstract

We have introduced some new types of nonsymmetric classical domains in Ref. 4, whose special cases are the examples of Ref. 3. In this chapter we discuss “extension spaces” for these domains. To define “extension space,” we introduce infinite distance points. In one complex variable, the Gauss plane can be compactified by introducing the unique infinite distance point, which is very convenient in many problems. In several complex variables, extension spaces for the four types of classical symmetric domains are well known. But for nonsymmetric domains, there is only Ref. 2.